Anisotropic Counts-in-Cells in Redshift Space: A New Route to Cosmological Constraints from Galaxy Surveys

Abstract

We introduce a novel extension of the volume-averaged correlation function (VACF) framework by replacing the traditional spherical smoothing kernels with anisotropic, ellipsoidal windows. This generalized approach enables the study of shape-dependent clustering statistics and captures directional information encoded in large-scale structure, particularly in redshift space where galaxy distribution is distorted by peculiar velocities. We define and compute ellipsoidal VACFs ${\bar{\xi }}_J(r_{\parallel },r_{\perp })$ and the corresponding reduced cumulants $s_J(r_{\parallel },r_{\perp })$, allowing for joint sensitivity to both scale and anisotropy across arbitrary statistical order J. Using a suite of COLA N-body simulations spanning a grid of cosmologies with varying ${\Omega }_M$ and ${\sigma }_8$, we analyze the behavior of ellipsoidal VACFs and cumulants in both real and redshift space. We find that the shape of the smoothing kernel that maximizes the clustering signal depends strongly on the redshift-space distortion regime: spherical in real space, prolate in the Fingers-of-God-dominated regime, and oblate in the Kaiser squashing-dominated regime. While the standard VACF amplitude is mainly sensitive to ${\sigma }_8$, the shape-dependence of redshift-space skewness shows a coherent response to the combined growth parameter $f{\sigma }_8$, with a typical sensitivity at the 1-3 $\sigma$ level between neighboring models. Our results demonstrate that ellipsoidal VACFs offer a computationally efficient and information-rich generalization of counts-in-cells analysis, with promising applications to galaxy survey data, halo catalogs, and cosmological tests of gravity beyond $\Lambda CDM$.

arXiv comment12 pages, 8 figures, 1 table. Code available at: https://github.com/Pawel-96/Avcorr

References in corpus (30)

• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• Observational Probes of Cosmic Acceleration
• Reconstructing the linear power spectrum of cosmological mass fluctuations
• A test of the nature of cosmic acceleration using galaxy redshift distortions
• Euclid. I. Overview of the Euclid mission
• Redshift-Space Distortions, Pairwise Velocities and Nonlinearities
• The 6dF Galaxy Survey: z \approx 0 measurement of the growth rate and sigma_8
• The WiggleZ Dark Energy Survey: the growth rate of cosmic structure since redshift z=0.9
• Fingers of God
• Biasing and Hierarchical Statistics in Large-scale Structure
• Baryon Acoustic Oscillations in 2D: Modeling Redshift-space Power Spectrum from Perturbation Theory
• Solving Large Scale Structure in Ten Easy Steps with COLA
• The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics
• Testing cosmological structure formation using redshift-space distortions
• The Bispectrum: From Theory to Observations
• Skewness and Kurtosis in Large-Scale Cosmic Fields
• The Luminosity-Weighted or `Marked' Correlation Function
• Skewness Induced by Gravity
• High-order galaxy correlation functions in the APM Galaxy Survey
• COLA with scale-dependent growth: applications to screened modified gravity models
• Self-similarity and scaling behavior of scale-free gravitational clustering
• Testing the theory of gravity with DESI: estimators, predictions and simulation requirements
• Hierarchical clustering in chameleon $f(R)$ gravity
• Mapping the real space distributions of galaxies in SDSS DR7: I. Two Point Correlation Functions
• Galaxy Bias and ${\sigma }_8$ from Counts in Cells from the SDSS Main Sample
• Revealing modified gravity signal in matter and halo hierarchical clustering
• The large-scale correlations of multi-cell densities and profiles, implications for cosmic variance estimates
• The matter density PDF for modified gravity and dark energy with Large Deviations Theory
• Skewness as a probe of Baryon Acoustic Oscillations
• Cosmology on point: modelling spectroscopic tracer one-point statistics